“…Water flows through small orifices (micro-orifice flows) are found in science, engineering, and many practical subjects, such as microfluidics [1,2,3,4], microfabrication [5], medical microbiology [6], biochemical analysis [7], microfluidic diagnostics [8], and drug delivery [9]. Micro-orifice flows have been investigated mainly in the field of fluid mechanics [10,11,12,13,14,15,16,17,18,19,20,21,22,23,24]. Recently, however, it has been reported that micro-orifice flows present complicated problems that are difficult to solve solely by fluid mechanics.…”